Geometry and Arithmetic

pp: 243–255

DOI: 10.4171/119-1/14

A note on a supersingular K3 surface in characteristic 2

Toshiyuki Katsura[1] and Shigeyuki Kondō[2]

(1) Hosei University, Tokyo, Japan
(2) Nagoya University, Japan

We construct, on a supersingular K3 surface with Artin invariant 1 in characteristic 2, a set of 21 disjoint smooth rational curves and another set of 21 disjoint smooth rational curves such that each curve in one set intersects exactly 5 curves from the other set with multiplicity 1 by using the structure of a generalized Kummer surface. As a corollary we have a concrete construction of a K3 surface with 21 rational double points of type A1 in characteristic 2.